In learned image compression methods, optimizing the network with different Lagrange multiplier (\(\lambda \) ) can trade off the distortion against the rate [1]}, [2]} and the learning goal of these methods can be formulated as:
\(\begin{split}\mathbb {L}_I &= R+\lambda D \\&\textup {with} \lambda \in \lbrace \lambda _1, \lambda _2, ..., \lambda _{n-1}, \lambda _{n}\rbrace ,\end{split}\) 
